Computational geometry emerged as a discipline in the seventies and has had considerable success in improving the asymptotic complexity of the solutions to basic geometric problems including constructions of data structures, convex hulls, triangulations, Voronoi diagrams and geometric arrangements as well as geometric optimisation. However, in the mid-nineties, it was recognized that the computational geometry techniques were far from satisfactory in practice and a vigorous effort has been undertaken to make computational geometry more practical. This effort led to major advances in robustness, geometric software engineering and experimental studies, and to the development of a large library of computational geometry algorithms, Cgal. The goal of this book is to take into consideration the multidisciplinary nature of the problem and to provide solid mathematical and algorithmic foundations for effective computational geometry for curves and surfaces. This book covers two main approaches. In a first part, we discuss exact geometric algorithms for curves and s- faces. We revisit two prominent data structures of computational geometry, namely arrangements (Chap. 1) and Voronoi diagrams (Chap. 2) in order to understand how these structures, which are well-known for linear objects, behave when defined on curved objects. The mathematical properties of these structures are presented together with algorithms for their construction. To ensure the effectiveness of our algorithms, the basic numerical computations that need to be performed are precisely specified, and tradeoffs are considered between the complexity of the algorithms (i. e. the number of primitive calls), and the complexity of the primitives and their numerical stability. Chap.
1100408739
Effective Computational Geometry for Curves and Surfaces
Computational geometry emerged as a discipline in the seventies and has had considerable success in improving the asymptotic complexity of the solutions to basic geometric problems including constructions of data structures, convex hulls, triangulations, Voronoi diagrams and geometric arrangements as well as geometric optimisation. However, in the mid-nineties, it was recognized that the computational geometry techniques were far from satisfactory in practice and a vigorous effort has been undertaken to make computational geometry more practical. This effort led to major advances in robustness, geometric software engineering and experimental studies, and to the development of a large library of computational geometry algorithms, Cgal. The goal of this book is to take into consideration the multidisciplinary nature of the problem and to provide solid mathematical and algorithmic foundations for effective computational geometry for curves and surfaces. This book covers two main approaches. In a first part, we discuss exact geometric algorithms for curves and s- faces. We revisit two prominent data structures of computational geometry, namely arrangements (Chap. 1) and Voronoi diagrams (Chap. 2) in order to understand how these structures, which are well-known for linear objects, behave when defined on curved objects. The mathematical properties of these structures are presented together with algorithms for their construction. To ensure the effectiveness of our algorithms, the basic numerical computations that need to be performed are precisely specified, and tradeoffs are considered between the complexity of the algorithms (i. e. the number of primitive calls), and the complexity of the primitives and their numerical stability. Chap.
109.99
In Stock
5
1
Effective Computational Geometry for Curves and Surfaces
344
Effective Computational Geometry for Curves and Surfaces
344Paperback(Softcover reprint of hardcover 1st ed. 2006)
$109.99
109.99
In Stock
Product Details
| ISBN-13: | 9783642069871 |
|---|---|
| Publisher: | Springer Berlin Heidelberg |
| Publication date: | 10/27/2010 |
| Series: | Mathematics and Visualization |
| Edition description: | Softcover reprint of hardcover 1st ed. 2006 |
| Pages: | 344 |
| Product dimensions: | 6.10(w) x 9.25(h) x 0.03(d) |
From the B&N Reads Blog